When the processing of a received sequence of data items, e.g. packets, is parallelised on multiple processing elements, the completion order of that parallel processing may not automatically correspond to the received order of the sequence of data items. However, preserving the original ordering of the sequence of data items may be important in some contexts, for example some network protocols do not handle packet reordering well. Deviations from the original ordering, i.e. late packets, are often treated as lost and retransmission may be requested, which decreases the system throughput and causes extra traffic and processing. In order to maintain the order of the received sequence of data items a reorder buffer (also referred to as a reorder window) may be used, the slots provided in the buffer being used to hold an ordered position for a given received data item while its processing is performed. However, when the technique is extended to a parallelised data processing environment using multiple processing elements the administration of reserving and releasing slots within the buffer will typically employ locking mechanisms, such that access to slots of the buffer by the multiple processing elements is carried out in mutual exclusion to avoid conflict. However, the use of such lock mechanisms does not scale well into a multiple processing element environment. A processing element seeking to complete and release multiple data items (i.e. to transfer the processed data items from the reorder buffer to an egress queue) will potentially prevent other threads from reserving locations in the reorder buffer (which they need to do to be able to start processing a new data item) or from completing and removing their own packets, wasting processing element resources. Indeed, bench marking has even shown negative scalability, wherein throughput decreases as more threads attempt to access the reorder buffer. Conversely, dedicating a single thread to handle the reordering results is likely to result in a single-threaded bottleneck.